Question

What is the solution in the following system? {×-y=11; -×+y=-11

Answer 1

[AI-generated answer — Bot GPT 3.5]

The given system of equations is:

{x - y = 11 ----(1)
(-x + y) = -11 ----(2)

Let's solve this system using the elimination method:

Adding equation (1) and equation (2):

(x - y) + (-x + y) = 11 + (-11)
x - y - x + y = 0
0 = 0

From this, we can see that both x and y are eliminated, and we are left with 0 = 0. This means that the given system of equations is dependent and has infinite solutions.

Answer 2

[AI-generated answer — Step-by-Step Bot]

To solve the system of equations {×-y=11; -×+y=-11} step-by-step, we will use the method of substitution.

Step 1: Start with the first equation ×-y=11 and solve for × in terms of y.
× = 11 + y

Step 2: Substitute the value of × in the second equation -×+y=-11 with 11 + y.
-(11 + y) + y = -11

Step 3: Simplify and solve for y.
-11 - y + y = -11
-11 = -11

Step 4: Both sides of the equation are equal, which means the system of equations is dependent. This implies that there are infinitely many solutions to the system.

Therefore, the solution to the system of equations {×-y=11; -×+y=-11} is any value of y, with × being equal to 11 plus the value of y.